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On extendability of additive code isometries
1. | IMATH, Université de Toulon, B.P. 20132, 83957 La Garde, France |
References:
[1] |
S. V. Avgustinovich and F. I. Solov'eva, To the metrical rigidity of binary codes,, Probl. Inf. Transm., 39 (2003), 178.
doi: 10.1023/A:1025148221096. |
[2] |
K. Bogart, D. Goldberg and J. Gordon, An elementary proof of the MacWilliams theorem on equivalence of codes,, Inf. Control, 37 (1978), 19.
doi: 10.1016/S0019-9958(78)90389-3. |
[3] |
R. C. Bose and R. C. Burton, A characterization of flat spaces in a finite geometry and the uniqueness of the Hamming and the MacDonald codes,, J. Combin. Theory, 1 (1966), 96.
doi: 10.1016/S0021-9800(66)80007-8. |
[4] |
I. Constantinescu and W. Heise, On the concept of code-isomorphy,, J. Geometry, 57 (1996), 63.
doi: 10.1007/BF01229251. |
[5] |
H. Q. Dinh and S. R. López-Permouth, On the equivalence of codes over rings and modules,, Finite Fields Appl., 10 (2004), 615.
doi: 10.1016/j.ffa.2004.01.001. |
[6] |
M. Greferath, A. Nechaev and R. Wisbauer, Finite quasi-Frobenius modules and linear codes,, J. Algebra Appl., 3 (2004), 247.
doi: 10.1142/S0219498804000873. |
[7] |
M. Greferath and S. E. Schmidt, Finite-ring combinatorics and MacWilliams equivalence theorem,, J. Combin. Theory Ser. A, 92 (2000), 17.
doi: 10.1006/jcta.1999.3033. |
[8] |
J. Gruska, Quantum Computing,, McGraw-Hill, (1999). Google Scholar |
[9] |
D. I. Kovalevskaya, On metric rigidity for some classes of codes,, Probl. Inf. Transm., 47 (2011), 15.
doi: 10.1134/S0032946011010029. |
[10] |
J. Luh, On the representation of vector spaces as a finite union of subspaces,, Acta Math. Acad. Sci. Hungar., 23 (1972), 341.
doi: 10.1007/BF01896954. |
[11] |
F. J. MacWilliams, Combinatorial Properties of Elementary Abelian Groups,, Ph.D thesis, (1962). Google Scholar |
[12] |
F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-correcting Codes,, North-Holland, (1977). Google Scholar |
[13] |
F. Solov'eva, T. Honold, S. Avgustinovich and W. Heise, On the extendability of code isometries,, J. Geometry, 61 (1998), 2.
doi: 10.1007/BF01237489. |
[14] |
H. N. Ward and J. A. Wood, Characters and the equivalence of codes,, J. Combin. Theory Ser. A, 73 (1996), 348.
doi: 10.1016/S0097-3165(96)80011-2. |
[15] |
J. A. Wood, Duality for modules over finite rings and applications to coding theory,, Amer. J. Math., 121 (1999), 555.
doi: 10.1353/ajm.1999.0024. |
[16] |
J. A. Wood, Foundations of linear codes defined over finite modules: The extension theorem and the MacWilliams identities,, in Codes over Rings (ed. P. Sóle), (2009), 124.
doi: 10.1142/9789812837691_0004. |
show all references
References:
[1] |
S. V. Avgustinovich and F. I. Solov'eva, To the metrical rigidity of binary codes,, Probl. Inf. Transm., 39 (2003), 178.
doi: 10.1023/A:1025148221096. |
[2] |
K. Bogart, D. Goldberg and J. Gordon, An elementary proof of the MacWilliams theorem on equivalence of codes,, Inf. Control, 37 (1978), 19.
doi: 10.1016/S0019-9958(78)90389-3. |
[3] |
R. C. Bose and R. C. Burton, A characterization of flat spaces in a finite geometry and the uniqueness of the Hamming and the MacDonald codes,, J. Combin. Theory, 1 (1966), 96.
doi: 10.1016/S0021-9800(66)80007-8. |
[4] |
I. Constantinescu and W. Heise, On the concept of code-isomorphy,, J. Geometry, 57 (1996), 63.
doi: 10.1007/BF01229251. |
[5] |
H. Q. Dinh and S. R. López-Permouth, On the equivalence of codes over rings and modules,, Finite Fields Appl., 10 (2004), 615.
doi: 10.1016/j.ffa.2004.01.001. |
[6] |
M. Greferath, A. Nechaev and R. Wisbauer, Finite quasi-Frobenius modules and linear codes,, J. Algebra Appl., 3 (2004), 247.
doi: 10.1142/S0219498804000873. |
[7] |
M. Greferath and S. E. Schmidt, Finite-ring combinatorics and MacWilliams equivalence theorem,, J. Combin. Theory Ser. A, 92 (2000), 17.
doi: 10.1006/jcta.1999.3033. |
[8] |
J. Gruska, Quantum Computing,, McGraw-Hill, (1999). Google Scholar |
[9] |
D. I. Kovalevskaya, On metric rigidity for some classes of codes,, Probl. Inf. Transm., 47 (2011), 15.
doi: 10.1134/S0032946011010029. |
[10] |
J. Luh, On the representation of vector spaces as a finite union of subspaces,, Acta Math. Acad. Sci. Hungar., 23 (1972), 341.
doi: 10.1007/BF01896954. |
[11] |
F. J. MacWilliams, Combinatorial Properties of Elementary Abelian Groups,, Ph.D thesis, (1962). Google Scholar |
[12] |
F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-correcting Codes,, North-Holland, (1977). Google Scholar |
[13] |
F. Solov'eva, T. Honold, S. Avgustinovich and W. Heise, On the extendability of code isometries,, J. Geometry, 61 (1998), 2.
doi: 10.1007/BF01237489. |
[14] |
H. N. Ward and J. A. Wood, Characters and the equivalence of codes,, J. Combin. Theory Ser. A, 73 (1996), 348.
doi: 10.1016/S0097-3165(96)80011-2. |
[15] |
J. A. Wood, Duality for modules over finite rings and applications to coding theory,, Amer. J. Math., 121 (1999), 555.
doi: 10.1353/ajm.1999.0024. |
[16] |
J. A. Wood, Foundations of linear codes defined over finite modules: The extension theorem and the MacWilliams identities,, in Codes over Rings (ed. P. Sóle), (2009), 124.
doi: 10.1142/9789812837691_0004. |
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